Has Inflation Become Harder to Forecast? James H. Stock Department of Economics, Harvard University and the National Bureau of Economic Research and Mark W. Watson* Woodrow Wilson School and Department of Economics, Princeton University and the National Bureau of Economic Research September 2005 *Prepared for the conference, “Quantitative Evidence on Price Determination,” Board of Governors of the Federal Reserve Board, September 29-30, Washington DC. We thank Jonas Fisher for bringing several of the issues discussed in this paper to our attention in a 1999 conversation, and Luca Benati for (more recent) helpful suggestions. This research was funded in part by NSF grant SBR-0214131.11. Introduction Forecasts of the rate of price inflation play a central role in the formulation of monetary policy, and forecasting inflation is a key job for economists at the Federal Reserve Board. This paper examines whether this task has become harder and, to the extent that it has, what have been the changes in the joint time series properties of inflation and its main predictors that have made it so. As it happens, inflation has both become harder and easier to forecast, depending on one’s point of view. On the one hand, inflation – like many other macroeconomic time series – has become much less volatile, so the root mean squared error of even naïve or relatively poor forecasts had declined since the mid-1980s. In this sense, inflation has become easier to forecast: the risk of inflation forecasts, as measured by mean squared forecast errors (MSFE), has fallen. On the other hand, the relative improvement of standard multivariate forecasting models, such as the backwards-looking Phillips curve, over a univariate benchmark has been smaller in percentage terms since the mid-1980s than before. This point was forcefully made by Atkeson and Ohanian (2001) (henceforth, AO), who found that backwards-looking Phillips curve forecasts were inferior to a naïve forecast of average twelve-month inflation by its average rate over the previous twelve months. In this sense, inflation has become harder to forecast, at least, it has become much more difficult for an inflation forecaster to provide value added beyond a univariate model. But what are the changes in the time series processes of inflation and its predictors that produced these changes? This paper proposes a parsimonious model of the changes in the univariate process for postwar U.S. quarterly inflation, in which inflation is represented as the sum of two components, a permanent stochastic trend component and a serially uncorrelated transitory component. Since the mid 1950s, there have been large changes in the magnitude of the permanent component of inflation – specifically, in the variance of the permanent disturbance – whereas the magnitude of the transitory component has been essentially constant. According to our estimates, the size of the permanent component was moderate from the mid 1950s through approximately 1970, it was large during the 1970s through 1983, it declined sharply in the mid 1980s to its value of the 1960s, and2since 1990 it declined further. Currently, the variance of the permanent disturbance is estimated to be at a record low since 1954. The time-varying trend-cycle model implies a time-varying first order integrated moving average (IMA(1,1)) model for inflation, in which the magnitude of the MA coefficient varies inversely with the ratio of the permanent to the transitory disturbance variance. Accordingly, the MA coefficient for inflation was small (approximately .25) during the 1970s but subsequently increased (the coefficient is .65 for the 1984-2004 period). The time-varying trend-cycle model of the univariate inflation process succinctly explains the main features of the historical performance of univariate inflation forecasts. During the 1970s the inflation process was well approximated by a low order autoregression (AR), but in the mid 1980s the coefficients of that autoregressions changed and, even if these changes are taken into account, the low order autoregression became a less accurate approximation to the inflation process since 1984. The changing AR coefficients and the deterioration of the low-order AR approximation accounts for the relatively poor performance of recursive and rolling AR forecasts in the 1984-2004 sample. Moreover, it turns out that the AO year-upon-year forecast, represented as a linear combination of past inflation, is close to the optimal linear combination implied by the post-1984 IMA model at the four-quarter horizon, although this is not the case at shorter horizons for the post-1984 period or any horizon for the pre-1984 period, cases in which the AO forecasts perform relatively poorly. This time-varying trend-cycle model also explains the excellent recent forecasting performance of an IMA model published by Nelson and Schwert (1977), which they estimated using data from 1953 to 1971. During the 1970s and early 1980s, the variance of the permanent component was an order of magnitude larger than it was in the 1950s and 1960s, and the Nelson-Schwert (1977) model ceased to be a good approximation. During the 1980s and 1990s, however, the size of the permanent component fell back to its earlier levels, and the Nelson-Schwert (1977) model was again a good approximation. The time-varying trend-cycle model also suggests a strategy for real-time univariate forecast. Currently the Nelson-Schwert (1977) forecast is performing very well, and the AO forecast is performing nearly as well, at least at long horizons. If the3importance of the permanent component were to change again, as it has in the past, the performance of these forecasts would deteriorate. The pseudo-out-of-sample results suggest that two approaches to time-varying trend-cycle models could be effective in the face of such changes, an unobserved components model with stochastic volatility, implemented using a nonGaussian filter, and an IMA(1,1) model with moving average coefficient estimated using a ten-year rolling window of past observations. The latter approach is simpler, but adapts to changing coefficients less quickly than, the former. The changing univariate inflation dynamics also help to explain the dramatic breakdown of recursive and rolling autoregressive distributed lag (ADL) inflation forecasts based on an activity measure. One reason for the deterioration